Algebra Examples

$(1 + 2 y i) (3 + i) + (1 + 2 y i) (6 - i)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Expand $(1 + 2 y i) (3 + i)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$1 (3 + i) + 2 y i (3 + i) + (1 + 2 y i) (6 - i)$

Step 1.1.2

Apply the distributive property.

$1 \cdot 3 + 1 i + 2 y i (3 + i) + (1 + 2 y i) (6 - i)$

Step 1.1.3

Apply the distributive property.

$1 \cdot 3 + 1 i + 2 y i \cdot 3 + 2 y i i + (1 + 2 y i) (6 - i)$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Multiply $3$ by $1$ .

$3 + 1 i + 2 y i \cdot 3 + 2 y i i + (1 + 2 y i) (6 - i)$

Step 1.2.2

Multiply $i$ by $1$ .

$3 + i + 2 y i \cdot 3 + 2 y i i + (1 + 2 y i) (6 - i)$

Step 1.2.3

Multiply $3$ by $2$ .

$3 + i + 6 y i + 2 y i i + (1 + 2 y i) (6 - i)$

Step 1.2.4

Multiply $2 y i i$ .

Tap for more steps...

Step 1.2.4.1

Raise $i$ to the power of $1$ .

$3 + i + 6 y i + 2 y (i^{1} i) + (1 + 2 y i) (6 - i)$

Step 1.2.4.2

Raise $i$ to the power of $1$ .

$3 + i + 6 y i + 2 y (i^{1} i^{1}) + (1 + 2 y i) (6 - i)$

Step 1.2.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 + i + 6 y i + 2 y i^{1 + 1} + (1 + 2 y i) (6 - i)$

Step 1.2.4.4

Add $1$ and $1$ .

$3 + i + 6 y i + 2 y i^{2} + (1 + 2 y i) (6 - i)$

Step 1.2.5

Rewrite $i^{2}$ as $- 1$ .

$3 + i + 6 y i + 2 y \cdot - 1 + (1 + 2 y i) (6 - i)$

Step 1.2.6

Multiply $- 1$ by $2$ .

$3 + i + 6 y i - 2 y + (1 + 2 y i) (6 - i)$

Step 1.3

Expand $(1 + 2 y i) (6 - i)$ using the FOIL Method.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$3 + i + 6 y i - 2 y + 1 (6 - i) + 2 y i (6 - i)$

Step 1.3.2

Apply the distributive property.

$3 + i + 6 y i - 2 y + 1 \cdot 6 + 1 (- i) + 2 y i (6 - i)$

Step 1.3.3

Apply the distributive property.

$3 + i + 6 y i - 2 y + 1 \cdot 6 + 1 (- i) + 2 y i \cdot 6 + 2 y i (- i)$

Step 1.4

Simplify each term.

Tap for more steps...

Step 1.4.1

Multiply $6$ by $1$ .

$3 + i + 6 y i - 2 y + 6 + 1 (- i) + 2 y i \cdot 6 + 2 y i (- i)$

Step 1.4.2

Multiply $- i$ by $1$ .

$3 + i + 6 y i - 2 y + 6 - i + 2 y i \cdot 6 + 2 y i (- i)$

Step 1.4.3

Multiply $6$ by $2$ .

$3 + i + 6 y i - 2 y + 6 - i + 12 y i + 2 y i (- i)$

Step 1.4.4

Multiply $2 y i (- i)$ .

Tap for more steps...

Step 1.4.4.1

Multiply $- 1$ by $2$ .

$3 + i + 6 y i - 2 y + 6 - i + 12 y i - 2 y i i$

Step 1.4.4.2

Raise $i$ to the power of $1$ .

$3 + i + 6 y i - 2 y + 6 - i + 12 y i - 2 y (i^{1} i)$

Step 1.4.4.3

Raise $i$ to the power of $1$ .

$3 + i + 6 y i - 2 y + 6 - i + 12 y i - 2 y (i^{1} i^{1})$

Step 1.4.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 + i + 6 y i - 2 y + 6 - i + 12 y i - 2 y i^{1 + 1}$

Step 1.4.4.5

Add $1$ and $1$ .

$3 + i + 6 y i - 2 y + 6 - i + 12 y i - 2 y i^{2}$

Step 1.4.5

Rewrite $i^{2}$ as $- 1$ .

$3 + i + 6 y i - 2 y + 6 - i + 12 y i - 2 y \cdot - 1$

Step 1.4.6

Multiply $- 1$ by $- 2$ .

$3 + i + 6 y i - 2 y + 6 - i + 12 y i + 2 y$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $3 + i + 6 y i - 2 y + 6 - i + 12 y i + 2 y$ .

Tap for more steps...

Step 2.1.1

Subtract $i$ from $i$ .

$3 + 6 y i - 2 y + 6 + 0 + 12 y i + 2 y$

Step 2.1.2

Add $3 + 6 y i - 2 y + 6$ and $0$ .

$3 + 6 y i - 2 y + 6 + 12 y i + 2 y$

Step 2.1.3

Add $- 2 y$ and $2 y$ .

$3 + 6 y i + 6 + 12 y i + 0$

Step 2.1.4

Add $3 + 6 y i + 6 + 12 y i$ and $0$ .

$3 + 6 y i + 6 + 12 y i$

Step 2.2

Add $3$ and $6$ .

$6 y i + 9 + 12 y i$

Step 2.3

Add $6 y i$ and $12 y i$ .

$18 y i + 9$